which data set has a mean of 35, median of 32, and a mode of 47?\n75, 35, 19, 20, 21, 25, 26, 35, 35\n68…

Explanation:

Step1: Recall mean, median and mode formulas

Mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, median is middle - value (for odd $n$) or average of two middle - values (for even $n$) after arranging data in ascending order, mode is the most frequently occurring value.

Step2: Check first option for mean, median and mode

For data set $75,35,19,20,21,25,26,35,35$:

• Mean: $\bar{x}=\frac{75 + 35+19+20+21+25+26+35+35}{9}=\frac{291}{9}\approx32.33$.
• Arranged in ascending order: $19,20,21,25,26,35,35,35,75$. Median is $26$. Mode is $35$. This is not the correct set.

Step3: Check second option for mean, median and mode

For data set $68,52,9,16,48,19,48,26,50$:

• Mean: $\bar{x}=\frac{68 + 52+9+16+48+19+48+26+50}{9}=\frac{336}{9}\approx37.33$.
• Arranged in ascending order: $9,16,19,26,48,48,50,52,68$. Median is $48$. Mode is $48$. This is not the correct set.

Step4: Check third option for mean, median and mode

For data set $70,60,50,80,70,32,35,35,35$:

• Mean: $\bar{x}=\frac{70+60 + 50+80+70+32+35+35+35}{9}=\frac{467}{9}\approx51.89$.
• Arranged in ascending order: $32,35,35,35,50,60,70,70,80$. Median is $50$. Mode is $35$. This is not the correct set.

Step5: Check fourth option for mean, median and mode

For data set $68,53,10,15,47,18,47,25,32$:

• Mean: $\bar{x}=\frac{68+53 + 10+15+47+18+47+25+32}{9}=\frac{315}{9}=35$.
• Arranged in ascending order: $10,15,18,25,32,47,47,53,68$. Median is $32$. Mode is $47$. This is the correct set.

For Question #2:

Step1: Arrange data in ascending order

The data set is $18,24,30,36,36,36$.

Step2: Find the median

Since $n = 6$ (even), median $=\frac{30 + 36}{2}=33$.

Answer:

Question #1: Fourth option $68,53,10,15,47,18,47,25,32$ Question #2: $33$